Use substitution to solve the following system of linear equations.
$4x+2y=7$
$x+5y=4$

• A. $\left(\frac12,\frac32\right)$
• B. $\left(\frac32,\frac12\right)$
• C. $\left(-\frac23,\frac13\right)$
• D. $\left(-\frac13,\frac23\right)$

Answer: (B)

Verified step by step guidance

1. Start by identifying the two equations in the system: Equation 1 is 4x + 2y = 7 and Equation 2 is x + 5y = 4.
2. Choose one of the equations to solve for one variable in terms of the other. Let's solve Equation 2 for x: x = 4 - 5y.
3. Substitute the expression for x from Step 2 into Equation 1. This gives: 4(4 - 5y) + 2y = 7.
4. Simplify the equation from Step 3 by distributing and combining like terms: 16 - 20y + 2y = 7.
5. Solve the simplified equation for y. Once you have the value of y, substitute it back into the expression for x from Step 2 to find the value of x.